I'd have to be stronger than the group in order to get more food than the entire group, but depending on their ability to cooperate I may be able to steal plenty for myself, an amount that would seem tiny compared to the large amount needed for the whole group.

The example I chose was a somewhat bad one I think though because the villagers would have a defender's advantage of protecting their food. You can substitute "food" for "abstract, uncontrolled resource" to clarify my point.